A triumphant Donald Trump accepted the Republican White House nomination on Thursday, promising fearful Americans to restore "safety" to a country mired in crises and losing its way.

Trump "humbly and gratefully" accepted the nomination before 2,000 raucous Republican Party activists in Cleveland, in a strikingly populist speech that offered a dark view of the American condition.

Between defining chants of "USA" and "Trump, Trump, Trump", the mogul-turned-TV-star-turned-politico cast himself as the "law and order candidate" and vowed to champion "people who work hard but no longer have a voice".

"I am your voice," he declared pointing into the cameras, promising a return to more secure times with "millions of new jobs and trillions in new wealth."

Tapping into public angst over recent racially-tinged shootings and seemingly indiscriminate terror attacks, Trump offered a tough-on-crime message that was reminiscent of Richard Nixon's election-winning strategy in 1968.

The "crime and violence that today afflicts our nation will soon, and I mean very soon, come to an end," he said.

"Beginning on January 20, of 2017, safety will be restored."

He repeated many of the controversial themes of his bruising primary campaign, banning foreigners from countries linked to terrorism, building a wall on the Mexican border, and renegotiating unfavorable trade deals with China.

The party rank-and-file lapped it up, rising to their feet in standing ovation after standing ovation and displaying none of the divisions that have plagued the four-day convention.

Clinton in focus

Trump's acceptance speech was his first major primetime address to the nation and the opening salvo of November's general election.

Nationwide polls put the New York mogul, who has never held elected office, almost neck-and-neck with Clinton, the former secretary of state heavily criticised over an email scandal. Clinton will formally accept the Democratic nomination at her own convention next week.

Trump painted her as corrupt, incompetent and hopelessly out of touch.

"This is the legacy of Hillary Clinton -- death, destruction, terrorism and weakness," he said.

Clinton fired off an icy rebuke on Twitter, telling him: "We are better than this." Throughout the Cleveland convention Republicans have rallied around chants of "lock her up".

Speakers had lined up to denounce Clinton for the deaths of their loved ones, for dodgy foreign policies, and for putting national security at risk by using a private email server for sensitive government information.

Trump accused the former secretary of state as being a political insider with "bad instincts" and "bad judgment."

"My message is that things have to change and they have to change right now."

"I'm with you, I will fight for you, and I will win for you."

It remains unclear if that message will be enough to unite a Republican Party riven with doubts over his candidature.

On Wednesday, those doubts were laid bare when his primary rival Ted Cruz pointedly refused to endorse him.

"Vote your conscience," Cruz said to a chorus of boos.

Before Trump took to the stage Friday, his daughter, Ivanka, tried to warm up the crowd and soften her father's image.

"He is colour blind and gender neutral. He hires the best person for the job. Period," she said.

"My father not only has the strength and ability necessary to be the next president, but also the kindness and compassion that will enable him to be the leader that this country needs."

But his roller-coaster campaign defeated 16 rivals and steamrolled stubborn party opposition after being written off as a joke.

He has shocked foreign leaders by questioning key pillars of American foreign policy. He recently hedged on normally sacrosanct support for NATO allies, warning it would depend "if they fulfill their commitments to us."

In office, Trump promised to "put America first."

Americans, he said, have "lived through one international humiliation after another."

"The most important difference between our plan and that of our opponents is that our plan will put America First."

"Americanism, not globalism, will be our credo," he said. "The American people will come first once again."